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An information theoretic treatment of Yager’s probability distribution negation
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DOI：10.1007/s00500-026-11413-9.png)
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Abstract
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In the seminal paper (Yager 2015), Yager defined the negation of a probability distribution $$\textbf{p}=(p_1,\dots ,p_n)$$ , as the distribution $$\overline{\textbf{p}} = (\overline{p}_1,\dots ,\overline{p}_n)$$ , where $$\overline{p}_i = ({1-p_i})/({n-1}),$$ for $$ i=1, \ldots , n.$$ In this paper, we present a comprehensive information-theoretic analysis of Yager’s negation and its generalizations. Using tools from information theory and majorization theory, we unify, extend, and strengthen a number of previously known properties of Yager’s negation within a common framework. Overall, our results offer strong theoretical justification for Yager’s negation as the most natural and principled definition of probability distribution negation under various information theoretic criteria.
Keywords:
Negation of a probability distribution
Uncertainty
Majorization
Schur-concave functions
\phi -entropies
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